Question

2 parallel sides of a Trapezium are 120 cm and 140 cm and other sides are 50 cm and 52 cm.Find the area of the trapezium.
PLEASE ANSWER - QUICK AS AN ARROW…………​

Answer 1

Step-by-step explanation:

ABCD is a trapezium, AB = 140 cm, BC = 52 cm, CD = 120 cm, DA = 50 cm.

Now, ACDE is a parallelogram.

BE = AB - DC

     = 140 - 120

     = 20 cm.

In ΔBEC,

Let a,b,c be the sides of the triangle.

∴ s = (a + b + c)/2

     = (50 + 20 + 52)/2

     = 61 cm

Area = √s(s - a)(s - b)(s - c)

        = √61(61 - 50)(61 - 20)(61 - 52)

        = √61(11)(41)(9)

        = 497.5 cm²

(i)

Area of ΔBEC:

497.5 = (1/2) * b * altitude

⇒ 497.5 * 2 = 20 * altitude

⇒ Altitude = 49.75 cm.

(ii)

Area of trapezium ABCD = (1/2) * Sum of parallel sides * Altitude

= (1/2) * (DC + AB) * h

= (1/2) * (120 + 140) * 49.75

= (1/2) * 260 * 49.75

= 6467.5 cm²

∴ Area of trapezium = 6467.5 cm²

Hope it helps!